Clarkson,P.C., FitzSimons,G.E., & Seah,W.T. (1999). Values Relevant to Mathematics? I’d Like to See That! In D.Tynam, N.Scott, K.Stacey, G.Asp, J.Dowsey, H.Hollingsworth & B.McCrae (Eds.), Mathematics: Across the ages. Melbourne: Mathematics Association of Victoria.

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Many schools are involved with developing Mission Statements. Such an activity can be very rewarding for a school. If handled well, it can be an opportunity for the community to come together to focus on what is it about their school that is unique and worthwhile. Within such a discussion, participants can rethink what they believe are the essentials of education and how these are implemented in their school. The notion then is for the Mission Statement to become a guiding statement for a reformation of the school.

But how is this played out when it comes to Mathematics? What can a statement of beliefs say about teaching of Mathematics? After all Mathematics is ‘value free’, since it deals with facts and facts alone. Or does it? What are the values that we also teach when it comes to Mathematics? Do we know that we teach these? Why do we teach these? What effects do they have on students? Should we be teaching other values?

In a school’s Mission Statement, there will be a certain number of statements that refer to those values, beliefs, attitudes in society that a particular school sees as important to foster. Hence it would not be unusual to see ideas of say ‘honesty’, and perhaps the notion of ‘working hard and this will be rewarded with academic success’, in a school’s Mission Statement. If the school is a private school and has affiliations with a particular religion, then we could expect to find in their Mission Statement other statements expounding extra values, beliefs, attitudes. So you might find expressions exhorting students, and the school community at large, of the centrality to life’s experience of belief in a church’s central doctrine for example.

Now when it comes to the actuality of life in a school, presumably these beliefs, attitudes, values embedded in a school’s Mission Statement are to be affirmed by what actually happens in the lived experience of teachers and students. Hence there is an assumption that within classrooms, such attitudes, beliefs and values will have an expression. Well we would expect and do see that in classrooms the notions of ‘honesty’ and the ‘working hard’ ethic are adhered to, although not always with the same verve. And clearly this is so in Mathematics classrooms as well as Language classes, Physical Education classes, and Religious Education classes: No difference in any of them.

But are these the only beliefs, values and attitudes that are affirmed by the life of a school? Clearly in religious sponsored schools we do see more of an emphasis on their particular beliefs in and out of religious education classes. However within government schools we also see beliefs and attitudes which may come not from those in the general community, but from the particular subject that is being studied, and from the normal practices associated with teaching a subject.

For example, when it comes to teaching physical education two of the beliefs, values or attitudes expected to be included in this subject area are that of living a healthy life style, and learning about the symbiotic relationship of competition and cooperation. We expect if we examine the physical education curriculum within a school for these notions to be explicitly addressed in various ways. Hence particular resources will be available and used so students can gain appropriate experiences which will help them construct ideas of what it means for them to deal with aggressive competition for example. If we went and observed the physical education teacher(s) [assuming the school can employ one of course] we would expect them to overtly discuss with their students aspects of a healthy life style as it can be live by those students. Likewise if we inspected the science curriculum in a school, listed off the resources used, and watched what the teachers did, we would expect to see values, beliefs and attitudes explicitly addressed in the course of teaching which attended to the notions of ‘the powerful place that science has in society’ through to ‘keeping careful notes of what you do when completing an experiment or conducting a field excursion’. Such beliefs, values or attitudes may not be exclusive to these particular subject areas, but we would expect these notions to be addressed by them.

In the brief discussion above it has been suggested that values, beliefs and attitudes are conveyed through a variety of means. We have suggested that at least three of these are: the way a school subject is structured, the chosen resources used in teaching including the text books used, and the teachers’ behaviours.

Then what about mathematics? What if any values, beliefs or attitudes are conveyed particularly within the teaching of this subject? Clearly we want the students to be honest about the work that they do. And we probably want them to work hard, or reasonably so. Most mathematics teachers would want students to work cooperatively with others, particularly when they are using small groups. But these are societal beliefs, attitudes or values that we would expect all subject teaching to contribute to. Is there any values to which mathematics teaching and learning have a particular, though not necessarily an exclusive contribution, to make in the ongoing growth of students? If there are any, do teachers recognise them? And do they set out to explicitly teach them?

Clearly there are different styles used in mathematics textbooks. Some seem to take the line that there are various rules that need to be learnt by the students. Such rules are boxed and highlighted with color. Rudimentary explanation is given at the most as to where such rules come from. It could be suggested that texts such as these may be valuing rules above understanding, and of elevating closure over openness. Perhaps it could be conjectured that schools and teachers who choose such texts also want such values emphasised. But do such teachers make such a choice of text with due consideration of the values that are embedded in them?

Moving from the use of resources to how teachers teach in the mathematics classroom, it is not unusual to imagine a situation where a mathematics teacher chooses to give extra marks on a test or for book work for neat presentation of work. What is the teacher valuing when this is done? On the other hand, what does this say about a teacher who says to students "That showing all your ‘fiddling around working’ in your books is just as important as making a clean copy of your final explanation"? We are not concerned at this point as to whether one or other of these approaches is correct, or in some way better overall, or one is better in this instance or that. But what underlies the difference in terms of the values that are being imparted? And does the teacher(s) know that in fact values are being imparted?

The crucial assumption behind this discussion is that if teachers have a higher awareness of what influences their decision making in classrooms, then they will be able to have more control over their decisions. There is some anecdotal evidence to suggest that often teachers do not explicitly recognise that one of the influences on their decision making in classrooms is the values they bring to the classroom. Hence they have less control of the process of decision making than they might. In turn then, if they became aware of the values they do bring into the classroom, then they will gain some extra measure of control.

In the last three paragraphs the term ‘values’ has been used deliberately, since a distinction is necessary between attitudes, beliefs and values. Values in this sense in mathematics education are the deep affective qualities which education fosters through the school subject of mathematics. There is a close relationship between values and attitudes, but with values occupying a more central and deeply held position than attitudes. As well there is a close correspondence between values and beliefs. But the distinction we make is that values are those affective qualities that are demonstrated in the actions that are carried out by a person, where as beliefs can be verbally assented to, but do not necessarily lead to observable behaviour in public. We suggest that this distinction is needed between beliefs and values, because it is often assumed in the literature that all beliefs do link to action. Clearly this is not so. Sometimes we hold contradictory beliefs at the same time. We have also all been in situations when we believe we should act in a particular way, but because of some impediment to such behaviour, we do not act at all. The simplistic definition of belief is one reason why the literature on mathematics teachers’ beliefs and what happens in mathematics classrooms is inconsistent and often confused.

What then of schools’ Mission Statements. They are useful documents. They can be an opportunity to get school communities thinking together. But they in themselves do not necessarily go far enough. Such Statements need to be interpreted at the teaching face within the school. They need elaboration into the different areas of the school’s operation. In our case such an elaboration needs to consider what are the deeply held affective qualities that a school wishes to actioned when Mathematics is being taught and learnt? In other words, the values that inevitably are brought to the mathematics teaching need to be explicit to the teachers, not implicit in their teaching.

Further information on a research project exploring this area with mathematics teachers (VAMP; Values and Mathematics Project) carried out jointly by Monash University and Australian Catholic University is available at the web site of http://www.education.monash.edu.au/projects/vamp/ Teachers interested in exploring further these notions can contact the team via this site. Papers listed in the references are also available from this site which detail further the thinking of the team.